Particles sliding on a fluctuating surface: phase separation and power laws

We study a system of hard-core particles sliding locally downwards on a fluctuating one-dimensional surface characterized by a dynamical exponent z and no overall tilt. In numerical simulations, an initially random particle density is found to coarsen and obey scaling with a growing length scale approximately t(1/z). The structure factor deviates from the Porod law for the models studied. The steady state is unusual in that the density-segregation order parameter shows strong fluctuations. The two-point correlation function has a scaling form with a cusp at small argument which we relate to a power law distribution of particle cluster sizes. Exact results on a related model of surface depths provide insight into this behavior.     

Study of multiparticle spikes in central 4.5A GeV/c C-Cu collisions

An analysis of local fluctuations, or spikes, is performed for charged particles produced in central C-Cu collisions at 4.5 GeV/c/nucleon. The distributions of spike centers and the maximum density distributions are investigated for different narrow pseudorapidity windows to search for multiparticle dynamical correlations. Two peaks over statistical background are observed in the spike-center distributions with the structure similar to that expected from the coherent gluon radiation model and recently found in hadronic interactions. The dynamical contribution to maximum density fluctuations is obtained to be hidden by statistical correlations, although behavior of the distributions shows qualitative agreement with that from the one-dimensional intermittency model. The observed features of the two different approaches, coherent vs. stochastic, to the formation of the local dynamical fluctuations are discussed.     

Local coupling of shell models leads to anomalous scaling

We consider cascade models of turbulence which are obtained by restricting the Navier-Stokes equation to local interactions. By combining the results of the method of extended self-similarity and a novel subgrid model, we investigate the inertial range fluctuations of the cascade. Significant corrections to the classical scaling exponents are found. The dynamics of our local Navier-Stokes models is described accurately by a simple set of Langevin equations proposed earlier as a model of turbulence [20]. This allows for a prediction of the intermittency exponents without adjustable parameters. Excellent agreement with numerical simulations is found.     

Density-PDFs and Lagrangian statistics of highly compressible turbulence

In isothermal, highly compressible turbulent flows, density fluctuations follow a log-normal distribution. We establish a connection between these density fluctuations and the probability-density-functions (PDF) of Lagrangian tracer particles advected with the flow. Our predicted particle statistics is tested against large scale numerical simulations, which were performed with 512³ collocation points and 2 million tracer particles integrated over several dynamical times.     

Formation of dense groups of particles in intermediate-energy nucleus-nucleus collisions

The formation of dense groups (fluctuations) of particles produced in the central CCu and MgMg collisions at the projectile momenta of, respectively, 4.5 and 4.3 GeV/c per nucleon is analyzed. The distributions of the maximum densities and of the centers of charged-particle fluctuations in pseudorapidity space are studied in searches for dynamical multiparticle correlations. The distributions of the centers show two peaks above the statistical background with a structure similar to that which is expected in the model of coherent gluon emission and which was observed in hadronic interactions. The charge independence of the distributions in question and an azimuthal isotropy of events involving pseudorapidity fluctuations are observed. The distributions of events with respect to the maximum density of fluctuations are governed primarily by the statistical contribution, although the behavior of the distributions in CCu collisions is in qualitative agreement with the prediction of the one-dimensional intermittency model. It is found that the resulting distributions are of a non-Poisson character both in CCu and in MgMg collisions. The results of this study indicate that, in describing local dynamical fluctuations in multiparticle production processes, the coherent and the stochastic approach supplement each other. The procedure employed in the analysis described here makes it possible to draw a direct comparison of the present results with the results of similar investigations of different reactions.     

Dynamics of a disordered, driven zero-range process in one dimension

We study a disordered, driven zero range process which models a closed system of attractive particles that hop with site-dependent rates and whose steady state shows a condensation transition with increasing density. We characterize the dynamical properties of the mass fluctuations in the steady state in one dimension both analytically and numerically and show that there is a dynamic phase transition in the density-disorder plane. We also determine the form of the scaling function which describes the growth of the condensate as a function of time, starting from a uniform density distribution.     

单事件的间歇分析

通过研究高能碰撞单事件间歇的分布情况,探讨了单事件间歇与相空间分割数及末态多重数之间的关系,给出了为能尽量消除统计起伏,得到反映单个事件动力学起伏的单事件间歇值所需满足的条件和应采用的方法.     

Effects of the Low Frequencies of Noise on On–Off Intermittency

A bifurcating system subject to multiplicative noise can exhibit on–off intermittency close to the instability threshold. For a canonical system, we discuss the dependence of this intermittency on the Power Spectrum Density (PSD) of the noise. Our study is based on the calculation of the Probability Density Function (PDF) of the unstable variable. We derive analytical results for some particular types of noises and interpret them in the framework of on-off intermittency. Besides, we perform a cumulant expansion (N. G. van Kampen, 24, 171 (1976).) for a random noise with arbitrary power spectrum density and we show that the intermittent regime is controlled by the ratio between the departure from the threshold and the value of the PSD of the noise at zero frequency. Our results are in agreement with numerical simulations performed with two types of random perturbations: colored Gaussian noise and deterministic fluctuations of a chaotic variable. Extensions of this study to another, more complex, system are presented and the underlying mechanisms are discussed. PACS Number: 05.40.-a, 05.45.-a, 91.25.-r     

Optimal precision of parameter estimation in images with local sub-Poissonian quantum fluctuations

Non-classical quantum effects allow light with local sub-Poissonian fluctuations below shot noise to be produced. We show that using such light can improve the estimation precision of a parameter in an image beyond the standard Poissonian limit. This benefit is theoretically investigated by means of a phenomenological model of local sub-Poissonian noise which assumes the independence of the fluctuations in each pixel. In particular, a bound on the best precision expectable independently of the exact unbiased estimation protocol used, which is given by the Cramer-Rao bound, is determined from this model. The numerical simulations presented in the special case of the estimation of a displacement of an image perturbed with local sub-Poissonian noise show that a standard estimator can overcome the classical Poissonian limit by reaching this limit precision only beyond a certain value of the photon flux which we characterize. We eventually present some numerical results that demonstrate the generality of the model proposed, of the optimality bounds and of the estimator performance.     

Comparison of particle production in Pb(158 GeV/nucleon)-AgBr collisions with the VENUS and FRITIOF models

Data on multiparticle production in interactions of 158 GeV/nucleon lead ions with the heavy nuclei in emulsions (Ag,Br) are compared with the predictions of the VENUS and FRITIOF models. It is found that total multiplicities of produced charged particles are reasonably well reproduced by both models. On the other hand, discrepancies between the data and the predictions are observed for the forward charge and pseudorapidity distributions. Furthermore, dynamical fluctuations, revealed in the data by application of the method of factorial moments, are absent from the model simulations. The dynamical fluctuations observed in the data can be at least partly due to Bose-Einstein correlations.     

Circuit implementation and multiform intermittency in ahyper-chaotic model extended from Lorenz system

<正>This paper presents a non-autonomous hyper-chaotic system,which is formed by adding a periodic driving signal to a four-dimensional chaotic model extended from the Lorenz system.The resulting non-autonomous hyper-chaotic system can display any dynamic behaviour among the periodic orbits,intermittency,chaos and hyper-chaos by controlling the frequency of the periodic signal.The phenomenon has been well demonstrated by numerical simulations,bifurcation analysis and electronic circuit realization.Moreover,the system is concrete evidence for the presence of Pomeau-Manneville Type-Ⅰintermittency and crisis-induced intermittency.The emergence of a different type of intermittency is similarly subjected to the frequency of periodic forcing.By statistical analysis,power scaling laws consisting in different intermittency are obtained for the lifetime in the laminar state between burst states.     

Dynamics of spherical particles on a surface: collision-induced sliding and other effects

We present a model for the motion of hard spherical particles on a two-dimensional surface. The model includes both the interaction between the particles via collisions and the interaction of the particles with the substrate. We analyze in detail the effects of sliding and rolling friction, which are usually overlooked. It is found that the properties of this particulate system are influenced significantly by the substrate-particle interactions. In particular, sliding of the particles relative to the substrate after a collision leads to considerable energy loss for common experimental conditions. The presented results provide a basis that can be used to realistically model the dynamical properties of the system, and provide further insight into density fluctuations and related phenomena of clustering and structure formation.     

Intermittency and fractals in nuclear collisions at 1.52 A GeV

The techniques of scaled factorial moments and multifractals have been employed to study the dynamical fluctuations of the produced singly charged particles in collisions of⁸⁴Kr ions at 1.52 A GeV in nuclear emulsion. The power law behaviors are observed in the data. The generalized dimensions are determined by using the methods of intermittency and multifractals.     

Chaotic transition in a three-coupled phase-locked loop system

The chaotic transition is observed in a three-coupled phase-locked loop (PLL) system in both experiments and numerical simulations. In this system, three PLL oscillators are connected with the periodic boundary condition. Intermittency is found in partially synchronized phase, in which two of three oscillators synchronize with each other and form a pair, and the chaotic transition occurs due to the recombination of synchronized pairs so that different pair is re-formed. In this phase, on-off intermittency is also observed and statistical analyses are carried out for on-off intermittent time series. This intermittency is considered as a hybrid type of intermittency with both on-off intermittency and intermittency due to the recombination of synchronized pairs present in the same time series. We also show the chaotic transition phenomena in a three-coupled logistic map system. (c) 2001 American Institute of Physics.     

Intermittency of energy in rapid granular shear flows

Hard-disk simulations are used for two-dimensional rapid granular shear flows of circular disks between two rotating cylinders. The intermittency effects associated with the rate of the energy dissipation of collisions are studied. The statistics of intermittent signals of energy dissipation reveals that a power law governs the dynamics of rapid shear granular flows. A dynamical system approach based on the Gledzer-Ohkitani-Yamada shell model of turbulence is employed to reproduce signals for energy dissipation that are statistically consistent with those from simulations. The results suggest that rapid granular flows can be analyzed by appropriate turbulent models.     

Lyapunov exponents and information dimension of the mass distribution in turbulent compressible flows

Turbulent density fluctuations in isothermal highly compressible turbulent flows are highly clumped and can be quantified by the scaling properties of powers of the mass distribution. This Eulerian quantity can be related to Lagrangian properties of the system given by the Lyapunov exponents of tracer particles advected with the flow. Using highly resolved numerical simulations, we show that the Kaplan-Yorke conjecture holds within numerical uncertainties.     

Lattice-Boltzmann Simulations of Particle-Fluid Suspensions

This paper reviews applications of the lattice-Boltzmann method to simulations of particle-fluid suspensions. We first summarize the available simulation methods for colloidal suspensions together with some of the important applications of these methods, and then describe results from lattice-gas and lattice-Boltzmann simulations in more detail. The remainder of the paper is an update of previously published work,^{(69, 70)} taking into account recent research by ourselves and other groups. We describe a lattice-Boltzmann model that can take proper account of density fluctuations in the fluid, which may be important in describing the short-time dynamics of colloidal particles. We then derive macro-dynamical equations for a collision operator with separate shear and bulk viscosities, via the usual multi-time-scale expansion. A careful examination of the second-order equations shows that inclusion of an external force, such as a pressure gradient, requires terms that depend on the eigenvalues of the collision operator. Alternatively, the momentum density must be redefined to include a contribution from the external force. Next, we summarize recent innovations and give a few numerical examples to illustrate critical issues. Finally, we derive the equations for a lattice-Boltzmann model that includes transverse and longitudinal fluctuations in momentum. The model leads to a discrete version of the Green–Kubo relations for the shear and bulk viscosity, which agree with the viscosities obtained from the macro-dynamical analysis. We believe that inclusion of longitudinal fluctuations will improve the equipartition of energy in lattice-Boltzmann simulations of colloidal suspensions.     

Braid theory and Zipf-Mandelbrot relation used in microparticle dynamics

A study is presented of the dynamics of a few body system of microparticles by using rank-ordering statistics in order to gain insight in the magneto-rheological properties of ferrofluids. This dynamical system is made up of micrometer sized plastic spheres dispersed in a ferrofluid driven by external magnetic fields. The world lines of the microspheres are captured and the dynamical modes are described by mathematical braid theory. Rank-ordering statistics on these modes shows a wide power law region consistent with the Zipf-Mandelbrot relation. We have also performed numerical simulations of the experimental system which show results in agreement with the observations.     

Intermittency route to rheochaos in wormlike micelles with flow-concentration coupling

We show experimentally that the route to chaos is via intermittency in a shear-thinning wormlike micellar system of cetyltrimethylammonium tosylate, where the strength of flow-concentration coupling is tuned by the addition of salt sodium chloride. A Poincaré first return map of the time series and the probability distribution of laminar lengths between burst events shows that our data is consistent with type-II intermittency. The coupling of flow to concentration fluctuations is evidenced by the "butterfly" intensity pattern in small angle light scattering (SALS) measurements performed simultaneously with the rheological measurements. The scattered depolarized intensity in SALS, sensitive to orientational order fluctuations, shows the same time dependence (like intermittency) as that of shear stress.